I have never tried breathing from my reg while its upside down in my mouth. I was taught that it would breathe wet. It appears that some will some wont. On the other hand I have been upside down and every other position and had no problems. The reg is upside down if Im upside down[turtleing]. Thats one that I cant explain. Any takers?
When you hand a reg off (such as when sharing air), the body of the reg is full of water. As I noted above, with the exhaust openings on the surfaceward side of the reg, at least some of the water (possibly most of the water) will remain in the reg even in spite of attempts to clear it. (The air just goes out the top, leaving the water below it in the reg.)
When you don't remove the reg from your mouth, there isn't much of any water in the body of the reg, so you can continue breathing even while inverted. Still, some regulators will let a bit of water leak in past the exhaust valves (usually when you're exhaling, but possibly just because the valves don't *quite* seal perfectly). If you have a very small amount of leakage into the reg body, you may be able to stay inverted for some time before there is enough water inside to feel "wet". However long it takes, eventually there *will* be noticeable water in the reg, and the only way to clear it will be to tip away from inverted so the water can be expelled through the exhaust.
One trick to inverted reg breathing that I learned on ScubaBoard is to punctuate your exhalations. Don't just breathe out and let your exhale very slowly come to a stop (which will leave the exhaust slightly open much longer, giving more opportunity for water ingress). Instead, breathe out normally, but end your exhale more on a final "T" sound. It's hard to describe, but it seemed to work on a wet-breathing reg I tried (on my own regs, I can breathe while inverted with no water ingress almost regardless of how I breathe).
Anyway, the point? Fully clearing a reg is very difficult or impossible with it inverted, which means that the already-stressed receiving diver is going to get a lovely gulp of water with their air -- a bad idea, to be sure. On the other hand, if the reg is clear, as long as it's sealed in your mouth, you should be able to breathe it while inverted with little difficulty (but again, if you need to clear it, you'll have to tip back for a moment).